The present invention relates to methods for monitoring processes utilizing an analytic model augmented with neural network, in combination with a statistical qualification technique that ensures modeling accuracy. More particularly, the invention is a system and method for monitoring a process on-line utilizing an integrated model comprised of an analytic representation of known process characteristics, a neural network for capturing unknown process characteristics, and a statistical technique for qualifying the remaining uncertainty of the combined neuro-analytic model. Known sequential probability ratio tests (SPORTS) are applied to the statistically qualified neuro-analytic (SQNA) model to achieve on-line monitoring capability and to evaluate deviant operating conditions for the process.
Traditional modeling of a process involves mathematically developing first principles knowledge of the process in the form of a set of equations that describe the state of the process according to laws of conservation and possibly experimental data. The first principles model is based on known physics of the process and is therefore often referred to as the analytic or physics-based model. A process is generally monitored by an on-line comparison between the real process output in the time domain and the artificial process output generated by the physics-based model. Differences between the real and artificial process outputs are interpreted to indicate a change in the state of the process.
Unfortunately, inaccuracies in physics-based models due to modeling errors caused by variations in process characteristics, uncertainties in the process, or simply the complexity of the process itself, adversely effect the ability to conduct reliable monitoring, such that changes in process performance remain undetected or normal changes cause false alarms. In addition, the development of an accurate, detailed physics-based model, especially for complex processes, is time, labor, and capital intensive. A more specific problem associated with physics-based modeling is the inability to accurately represent the characteristics of the process after the initial start-up period, when the operating characteristics of the process have stabilized. Performing first principle studies on processes that are installed and operating is impractical, as correcting modeling errors in response to actual operating conditions is generally accomplished at a significant expense.
An alternative approach for modeling a process, particularly where process uncertainties exist, is to measure input and output values for the process and develop a process model based on the measured input-output mappings, irrespective of the underlying process characteristics. This approach is accomplished by an artificial intelligence technique: neural networking. Neural networks involve a large number of processors operating in parallel. The neural network is trained by processing large amounts of data and rules about data relationships, whereby a network learning rule is established that allows the network to adjust its connection weights in order to associate given input vectors with corresponding output vectors and to minimize the difference between real and expected output values. Currently, neural networks are employed in a wide range of applications, including speech synthesis, pattern recognition, oil exploration data analysis, weather prediction, and interpretation of nucleotide sequences, among others.
Recently, physics-based models have been combined with neural networks to better adapt the monitoring system to actual process events. A great advantage of a neural network augmented physics-based model is the inclusion of prior results, or process experience, into the monitoring system. U.S. Pat. No. 5,673,368 issued to Broese, et al. describes an augmented physics-based model for process control that continuously modifies a single parameter in the physics-based model by reducing the deviation between the mathematically computed physics-based model output and the measured, or actual, process output. The deviation is reduced after each process cycle by first supplying measured input values that influence variable parameters of the physics-based model to a neural network, whereby the neural network adaptively improves the computed results, and, next, adjusting the first principles model parameters in response to the neural network output. The Broese model, however, does not statistically qualify the accuracy of the model, which is important for a process experiencing random variations due to noise or modeling inaccuracies. In other words, the Broese model provides no mechanism for confirming that the augmented model is statistically consistent with the measured process output.
The present invention is a new and significantly improved method for monitoring complex, non-linear processes by combining traditional physics-based modeling, neural networks, and statistical techniques to overcome the disadvantages of physics-based models and physics-based models augmented by neural networks. The present statistically qualified neuro-analytic (SQNA) model provides a more sensitive and reliable process monitoring system that conforms more closely to the actual operating condition of the process, such that incipient failure conditions are more readily identified.
Therefore, in view of the above, a basic object of the present invention is to provide a method for monitoring a process that incorporates physics-based modeling, neural networking, and statistical qualification techniques to achieve significantly improved monitoring performance, e.g., reduced false alarms and/or increased detection sensitivity.
Another object of this invention is to provide an accurate and reliable on-line method for monitoring a process or apparatus having a high level of uncertainty.
Another object of this invention is to provide a statistically qualified neuro-analytic modeling system for complex processes that cannot be adequately represented by traditional modeling techniques, including physics-based modeling and/or neural network modeling.
Yet another object of this invention is to provide a method for monitoring a process, including providing statistical qualification of the accuracy of the model.
Additional objects, advantages and novel features of the invention will be set forth in the description which follows and will become apparent to those skilled in the art upon examination of the following or may be learned by practice of the invention. The objects and advantages of the invention may be realized and attained by means of instrumentation and combinations particularly pointed out in the appended claims.
Briefly, the present method for monitoring a process involves applying a unique statistically qualified neuro-analytic (SQNA) model to a process having known and unknown characteristics for accurately and reliably identifying changes in the process state. The SQNA monitoring system is developed in two general steps: deterministic model adaption and stochastic model adaptation. The developed SQNA model is validated using known sequential probability ratio tests (SPRT), e.g., Wald""s SPRT, and applied to the process as an on-line monitoring system.
Deterministic model adaption involves first formulating a physics-based model, also referred to as the analytic model, that represents the certain, known characteristics of the process to be monitored in the form of a state equation and an output equation. Next, a neural network is incorporated into the analytic model by adding neural network vector functions to the analytic model state and output equations, such that the uncertain, unknown characteristics of the process are represented in the resulting combined neuro-analytic model. The neuro-analytic model is trained by adjusting the neural network weights according to a unique scaled equation error minimization technique, producing a trained neuro-analytic model that is closely adapted to the actual operating state of the process.
Stochastic model adaptation involves qualifying any remaining uncertainty in the trained neuro-analytic model resulting from factors such as changing process dynamics during data collection, lingering unmodeled process state variables, and/or process input and output noise, among others. Stochastic model adaptation is accomplished by first describing the error (e.g., process input/output noise and state uncertainty) in the state and output equations of the neuro-analytic model by inserting independent random vectors representing the error into the state and output equations of the neuro-analytic model. The resulting state and output equations are linearized, and a single equation comprising only independent variables is written, referred to as the error propagation formula, that describes the propagation of the error (e.g., process input/output noise and state uncertainty) to the output equation. Remarkably, the state equation has been eliminated from the error propagation equation.
Next a likelihood function is written for maximizing the likelihood that the neuro analytic model generates the actual measured process output. The likelihood function is formulated from the error propagation equation by estimating the variances of the process noise (input/output) and state uncertainty random vectors, and an iterative scheme is used to determine the maximum likelihood solution, or, alternatively, the minimum of the negative of the log likelihood function. Thus, the likelihood function is used to statistically qualify, or calibrate, the trained neuro-analytic model of the process.
In the preferred embodiment, known statistical techniques, such as Wald""s SPRT, are used to confirm that the statically qualified neuro-analytic (SQNA) model accurately describes the actual process. Wald""s SPRT may also be used to apply the SQNA model on-line to monitor for chances in the process state.
Advantageously, the present SQNA model has improved process monitoring performance, such that false alarms and failures to detect process anomalies are minimized.